Practical applications of Haselgrove's equations for HF systems

Jenifer Haselgrove's 1955 paper, entitled “Ray Theory and a New Method for Ray Tracing,” has become the classic reference for the application of Hamilton's equations to the problem of ionospheric radiowave propagation. Her formulation provides a computationally tractable means for analyzing radiowave propagation when ionospheric refraction is a significant effect, as is the case in the high- frequency (HP: 3-30 MHz) band, where shortwave communication systems and over-the-horizon (OTH) radars operate. The study of HP propagation effects on communications and radar systems has formed a substantial portion of my career, and so it is with pleasure that I review the more significant aspects of that work to honor Jenifer Haselgrove (now Jenifer Leech) for her very significant contribution, Haselgrove’ s Equations. I discuss the extension of Haselgrove's Equations for accurate computation of ray focusing and ray homing, and the application of Haselgrove's Equations in HP propagation-channel modeling, simulation of Doppler-spread surface clutter for OTH radar, geo location of targets for OTH radar, and the mitigation of traveling ionospheric disturbances (TIDs) for OTH radar.